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This paper is concerned with the optimal state estimation problem for a class of time-varying uncertain dynamical networks with mixed time-delay under uncertain probabilities. Here, the mixed time-delays include the constant time-delay and the random sensor delay, where the random sensor delay is depicted by a Bernoulli distributed random variable and the occurrence probability of the random sensor delay can be uncertain. The major novelty of the paper lies in that a new time-varying state estimation algorithm is given such that, for all parameter uncertainties, mixed time-delays and uncertain probabilities, a locally optimal upper bound of the estimation error covariance is obtained and the desirable estimator parameter of easy-to-implement feature is designed. Moreover, the performance evaluation problem of the presented estimation algorithm is solved, where the monotonicity analysis is shown regarding the trace of the upper bound and the deterministic occurrence probability of random sensor delay. At last, the simulations are given to show the validity and correctness of the proposed time-varying estimation method. In particular, the comparisons are given to show the relationship of the upper bound and occurrence probability.

Optimized State Estimation of Uncertain Linear Time-Varying Complex Networks With Random Sensor Delay Subject to Uncertain Probabilities